I'm very busy at work, now,
I am grounded at work?
I am grounded in the office?
or I am grounded at the office?
thanks,
The term "grounded" originates as a term used among pilots/in aviation to describe disciplinary action for some violation of rules in which they may not fly for a period of time. It is currently also used to describe a penalty imposed by parents on a child/teenager in which the child/teenager may not leave their home for a period of time because of some transgression. You will seldon/never hear/read it used as in your examples.
billmcd has explained how we use grounded, and it doesn't really cover your situation. You are stuck at/in the office.
Context is always important; labelling is rarely important.
Or you're buried in work, or you're swamped. But you're not grounded.